A376501 - OEIS

%I #15 Oct 23 2024 16:27:32

%S 241,281,283,401,421,461,463,467,601,607,641,643,647,683,809,821,823,

%T 863,1021,1049,1061,1069,1201,1249,1283,1409,1429,1487,1601,1609,1823,

%U 1847,2011,2027,2039,2161,2207,2347,2389,2411,2417,2441,2459,2473,2503,2543,2617,2657,2671,2677,2699,2707

%N Primes that contain at least two different even digits where any permutation of the even digits leaving the odd digits fixed produces a prime. See comments for the treatment of 0.

%C Primes for which permutations described in the name produce primes with leading 0s are in the sequence but the generated primes with leading 0s are not. For example, a transposition in 401 produces 041, hence 401 is in the sequence but 41 is not.

%H Robert Israel, <a href="/A376501/b376501.txt">Table of n, a(n) for n = 1..10000</a>

%e 2027, 2207 are primes and 227 is prime with a leading 0 generated by permuting even digits in either 2027 or 2207.  Hence 2027 and 2207 are in the sequence but 227 is not due to the leading 0.

%e 6067, 6607 are primes but 667 generated by permuting even digits in either 6067 or 6607 is not prime, hence by name, neither number is in the sequence.

%p filter:= proc(n) local L,oddi,eveni,xodd,i;

%p  if not isprime(n) then return false fi;

%p  L:= convert(n,base,10);

%p  oddi,eveni:= selectremove(t -> L[t]::odd,[$1..nops(L)]);

%p  if nops(convert(L[eveni],set))<2 then return false fi;

%p  xodd:= add(10^(i-1)*L[i],i=oddi);

%p  andmap(t -> isprime(xodd+add(10^(eveni[i]-1)*L[t[i]],i=1..nops(eveni))), combinat:-permute(eveni))

%p end proc:

%p select(filter, [seq(i,i=3..10000,2)]); # _Robert Israel_, Oct 23 2024

%Y Cf. A000040, A003459, A376500, A376502.

%K nonn,base

%O 1,1

%A _Enrique Navarrete_, Sep 25 2024